Final answer:
Calculate the total wall area that needs painting and multiply by 3 for the number of coats. Divide the total area by the coverage of one gallon of paint and round up to the nearest whole number to determine 12 gallons are needed.
Step-by-step explanation:
To calculate the amount of paint needed, we need to first determine the total area that needs to be painted in the room. The dimensions of the room are 20 feet by 8 feet with a wall height of 10 feet. There are two longer walls and two shorter walls in a rectangular room, so we calculate their areas separately and then add them together.
The area of one long wall is 20 feet x 10 feet = 200 square feet. Since there are two long walls, their combined area is 2 x 200 square feet = 400 square feet.
The area of one short wall is 8 feet x 10 feet = 80 square feet. Similarly, the two short walls together have an area of 2 x 80 square feet = 160 square feet.
The total wall area to be painted is 400 square feet + 160 square feet = 560 square feet for one coat. Since the room needs 3 coats of paint, we need to cover 560 square feet x 3 = 1,680 square feet in total.
A gallon of paint covers 150 square feet, so to find out how many gallons are needed, divide the total area by the coverage of one gallon:
1,680 square feet / 150 square feet per gallon = 11.2 gallons
Since we cannot buy 0.2 of a gallon, we need to round up to the nearest whole number. Therefore, 12 gallons of paint should be purchased to complete the job.